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Natural Science and Advanced Technology Education

“Tap, Tap Water”. Quantum Tunneling Demonstration

Katarina Borković, Andreana Ćurić

Published Aug 1, 2022• 0 citations

Abstract

Quantum tunneling is a phenomenon in which an atom or a subatomic particle appears on the other side of a potential barrier that should be impenetrable to the particle, given the difference between the kinetic energy of the particle and the potential energy of the barrier, the former being significantly lesser. However, if the barrier shrinks enough the particle will be able to tunnel right through it. This is among the most well-known quantum physics phenomena. Historically, physicists struggled to grasp the wavelike and particle-like duality of light and subatomic particles. The aforementioned phenomenon occurs due to the wavelike behavior of photons. Quantum phenomena, such as quantum tunneling, might appear quite convoluted, therefore a simple experimental demonstration was performed to highlight the basic mechanisms of the phenomenon in a manner comprehensible to the wide masses. The demonstration, however, is just what we are in fact observing instead of quantum tunneling – “optical tunneling”, perhaps more commonly known as Frustrated Total Internal Reflection (FTIR). This mathematically analogous phenomenon serves as a mere tool for explaining quantum tunneling while aiding our understanding of it and facilitating its visualization. The experimental demonstration shall prove that quantum tunneling is a daily occurring phenomenon and that it is possible once the barrier is thin enough. If these arguments are indeed met with a successful visual demonstration a wavelike character of the photons happens to be confirmed as well.

DOI: 10.53656/nat2022-4.04

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Tunneling is an outstanding physical process. The observation that particles surmount a high barrier in spite of the fact that they don't have the necessary energy can not be explained by classical physics. However, this so called tunneling became allowed by quantum mechanics. Experimental tunneling studies with different photonic barriers from microwave frequencies up to ultraviolet frequencies point towards a universal tunneling time [1, 2]. Tunneling can be described by virtual, that is, by unobservable particles [3]. In the case of tunneling there is a virtual particle between the real incident and the real transmitted particles. Tunneling modes are solutions of the Schrödinger and of the Helmholtz equations. The most prominent example of the occurrence of tunneling modes in optics is frustrated total internal reflection (FTIR) at double prisms. In 1949 Sommerfeld [4] pointed out that this optical phenomenon represents the analogy of quantum mechanical particle tunneling. Recent experimental and theoretical data confirmed the conjecture that the tunneling process is characterized by a universal tunneling time presumably independent of the kind of field. The observed tunneling processes proceeded at a time of the order of magnitude of the reciprocal frequency of the wave packets.

Abstract Tunneling is an outstanding physical process. The observation that particles surmount a high barrier in spite of the fact that they don't have the necessary energy can not be explained by classical physics. However, this so called tunneling became allowed by quantum mechanics. Experimental tunneling studies with different photonic barriers from microwave frequencies up to ultraviolet frequencies point towards a universal tunneling time [1, 2]. Tunneling can be described by virtual, that is, by unobservable particles [3]. In the case of tunneling there is a virtual particle between the real incident and the real transmitted particles. Tunneling modes are solutions of the Schrödinger and of the Helmholtz equations. The most prominent example of the occurrence of tunneling modes in optics is frustrated total internal reflection (FTIR) at double prisms. In 1949 Sommerfeld [4] pointed out that this optical phenomenon represents the analogy of quantum mechanical particle tunneling. Recent experimental and theoretical data confirmed the conjecture that the tunneling process is characterized by a universal tunneling time presumably independent of the kind of field. The observed tunneling processes proceeded at a time of the order of magnitude of the reciprocal frequency of the wave packets.

‘Tunnelling’ is the metaphorical name given to the process, possible in quantum mechanics, but not in classical mechanics, whereby a particle can disappear from one side of a potential-energy barrier and appear on the other side without having enough kinetic energy to mount the barrier. One can think of this as a manifestation of the wave-nature of particles. The wavelength is larger if a particle is lighter. In particular electrons, being very light compared to atoms, have wavelengths as large or larger than atoms at energies found in the valence shells of molecules. Thus, they easily ooze through and around atoms and molecules. We are also concerned with the tunnelling of heavy particles: nuclei, atoms, molecules.

When we dealt with the finite potential well in the last chapter, it was observed that the wave function penetrated into the barriers. This process does not occur in classical mechanics, since a particle will actually bounce off the barrier. However, when we treat the particle as a wave, then the wave nature of barrier penetration can occur. This is familiar in electromagnetic waves, where the decaying wave (as opposed to a propagating wave) is termed an evanescent wave. For energies below the top of the barrier, the wave is attenuated, and it decays exponentially. Yet, it takes a significant distance for this decay to eliminate the wave completely. If the barrier is thinner than this critical distance, the evanescent wave can excite a propagating wave in the region beyond the barrier. In optics, this effect is termed frustrated total internal reflection . We are familiar with total internal reflection just from a swimming pool. Water has a higher dielectric constant than free space, so when we are under water, there is critical angle beyond which we can no longer see out (from under the water) of the pool. In optics, we can use a prism, and there will be reflection from the back surface for angles greater than a critical angle. The wave in back of the prism is attenuated and decaying. But, if we place another high dielectric constant material close to the prism, the decaying wave can excite a wave in this new material. 1 Thus, the wave can penetrate the barrier and continue to propagate, with an attenuated amplitude, in the trans-barrier region. For particles, this process is termed tunneling , with analogy to the miners who burrow through a mountain in order to get to the other side! In fact, it is known that the nuclear fusion process by which our sun produces its power would not occur were there no tunneling. The intra-nuclear repulsion is just too strong and tunneling is required for the nuclei to find one another.

Everyday macroscopic objects follow the laws of classical mechanics. For microscopic objects, such as atoms or nuclei, the wave character of their dynamics has to be taken into account within the framework of quantum mechanics. While wave-like behaviour can show up in various ways, one of the most striking is the tunnelling effect: some events that are classically forbidden for energetic reasons happen because the quantum particles can tunnel under a potential barrier. Similarly, events that are prohibited due to some other dynamical constraints can occur via a process known as dynamical tunnelling. Indeed, tunnelling plays a major role in a variety of physical phenomena, ranging from α-particle radioactivity to the current–voltage characteristics of transistors.

Frustrated Total Internal Reflection (FTIR) has been researched since the time of Sir Issac Newton. In this paper, its application in modern optics is reviewed. A theoretical description of the phenomenon is presented beginning with Snell’s Law. The analogy between FTIR and quantum tunneling in one dimension is discussed. A quantitative and inexpensive method of demonstrating FTIR based on the attenuation of a microwave through an air gap between two wax prisms is described and a quantitative comparison of the theory with experiment is made. An extension of FTIR using microwave, as it is used in an Evanescent Wave Atomic Force Microscope (EW-AFM), is looked into and evaluated.